As President Biden was planning a politically risky trip to Saudi Arabia this summer, his top aides thought they had struck a secret deal to boost oil production through the end of the year — an arrangement that could have helped justify breaking a campaign pledge to shun the kingdom and its crown prince.

It didn’t work out that way.

Mr. Biden went through with the trip. But earlier this month, Saudi Arabia and Russia steered a group of oil-producing countries in voting to slash oil production by two million barrels per day, the opposite of the outcome the administration thought it had secured as the Democratic Party struggles to deal with inflation and high gas prices heading into the November elections.

The move led angry Biden administration officials to reassess America’s relationship with the kingdom and produced a flurry of accusatory statements between the two governments — including a charge by the White House that Saudi Arabia was helping Russia in its war in Ukraine.